MHB How Do Vieta's Formulas Apply to Cubic Polynomial Roots?

[Mathsonfire]

88

 

[MountEvariste]

You can read $\alpha + \beta + \gamma $, $\alpha\beta +\alpha \gamma + \beta \gamma$ and $\alpha \beta \gamma$ off from the polynomial.

Now what's $(\alpha+\beta)+(\alpha+\gamma)+(\beta+\gamma)$?

And what's $(\alpha+\beta)(\alpha+\gamma)(\beta+\gamma)$?

And finally $(\alpha+\beta)(\alpha+\gamma)+(\beta+\gamma)(\alpha + \beta)+(\alpha+\gamma)(\beta+\gamma)$?Those questions all seem to be an exercise in Vietas formulas.